Theorem orim2d 789

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 787	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  790  orbi2d  791  pm2.82  813  stdcndcOLD  847  pm2.13dc  886  exmid1dc  4243  acexmidlemcase  5929  poxp  6308  fodjuomnilemdc  7228  omniwomnimkv  7251  exmidontriimlem1  7315  indpi  7437  suplocexprlemloc  7816  nneoor  9457  uzp1  9664  maxabslemlub  11437  xrmaxiflemlub  11478  nninfctlemfo  12280  exmidunben  12716  bj-nn0suc  15764  sbthomlem  15828